Many efforts to persuade others politically employ interpersonal conversations. A recurring question is whether the participants in such conversations are more readily persuaded by others who share their demographic characteristics. Echoing concerns that individuals have difficulties communicating across differences, research finds that individuals perceive demographically similar people as more trustworthy, suggesting shared demographics could facilitate persuasion. In a survey of practitioners and scholars, we find many share these expectations. However, dual-process theories suggest that messenger attributes are typically peripheral cues that should not influence persuasion when individuals are effortfully thinking, such as during interpersonal conversations. Supporting this view, we analyze data from eight experiments on interpersonal conversations across four topics (total N = 6, 139) and find that shared demographics (age, gender, or race) do not meaningfully increase their effects. These results are encouraging for the scalability of conversation interventions, and suggest voters can persuade each other across differences.